Problem: Simplify the following expression: $ z = \dfrac{-5y}{-2y + 10} + \dfrac{-9}{7} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-5y}{-2y + 10} \times \dfrac{7}{7} = \dfrac{-35y}{-14y + 70} $ Multiply the second expression by $\dfrac{-2y + 10}{-2y + 10}$ $ \dfrac{-9}{7} \times \dfrac{-2y + 10}{-2y + 10} = \dfrac{18y - 90}{-14y + 70} $ Therefore $ z = \dfrac{-35y}{-14y + 70} + \dfrac{18y - 90}{-14y + 70} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{-35y + 18y - 90}{-14y + 70} $ $z = \dfrac{-17y - 90}{-14y + 70}$ Simplify the expression by dividing the numerator and denominator by -1: $z = \dfrac{17y + 90}{14y - 70}$